Multifrequency Electromagnetic Data Interpretation for Subsurface Characterization

Multifrequency Electromagnetic Data Interpretation for Subsurface Characterization
Copyright
Dedication
Contents
Preface
Acknowledgments
Section 1
1. Multifrequency electromagnetic data acquisition and interpretation in the laboratory and in the subsurface: A comprehensive ...
1. Electromagnetic measurements in the laboratory
1.1 Devices and materials
1.2 Data acquisition and data type
2. Case studies on the use of core-scale and laboratory-scale multifrequency electromagnetic measurements
2.1 Case study I
2.2 Case study II
2.3 Case study III
2.4 Case study IV
3. Multifrequency electromagnetic measurements in the subsurface
3.1 Devices and materials
3.2 Data acquisition and data type
4. Case studies on the use of near-wellbore and field-scale multifrequency electromagnetic measurements in the subsurface
4.1 Case study I
4.2 Case study II
4.3 Case study III
4.4 Case study IV
4.5 Case study V
5. Electromagnetic log-interpretation methodologies for subsurface characterization
5.1 Electromagnetic log-interpretation methodologies for conventional formations
5.2 Electromagnetic log-interpretation methodologies for turbiditic formation
5.3 Electromagnetic log-interpretation methodologies for shaly-sand formation
5.4 Electromagnetic log-interpretation methodologies for carbonate formation
5.5 Electromagnetic log-interpretation methodologies for unconventional formation characterization
5.6 Electromagnetic interpretation methodologies for pore-scale digital rock
6. Cases on the use of electromagnetic measurements with other types of measurement
6.1 Joint interpretation of electromagnetic measurements with nuclear magnetic resonance measurements
6.2 Joint interpretation of electromagnetic measurements with wireline formation tester measurements
6.3 Joint interpretation of electromagnetic measurements with sonic or seismic measurements
7. Conclusions
References
2. Petrophysical models for the interpretation of electromagnetic logs: A brief review
1. Archie, Simandoux, Waxman–Smits, and Dual water model
2. Complex refractive index and Lichteneker-Rother model
3. Effective medium models (mixing formulas)
3.1 Stroud-Milton-De model
3.2 Bimodal model
3.3 Maxwell–Garnet model
3.4 Hanai–Bruggeman formula
3.5 Clay-particle model for shaly-sand formations
3.6 Wideband electromagnetic dispersion model
3.7 Shaly-sand model
3.8 Textural model
4. Use of petrophysical models for interpreting electromagnetic measurements on core samples
4.1 Case study 1
4.2 Case study 2
Symbols and abbreviations
References
Section 2
3. Multifrequency conductivity and permittivity of porous material containing non-conductive particles possessing surface cond ...
1. Interfacial polarization phenomenon because of nonconductive particles possessing surface charge
2. Mechanistic model of interfacial polarization of nonconductive particle possessing surface charge
3. Model of interfacial polarization because of nonconductive particle possessing surface charge
3.1 Model description
3.2 Assumptions
3.3 Mechanistic model development
3.3.1 Poisson-Nernst-Planck equation
3.3.2 Solution of Helmholtz partial differential equations
3.3.3 Solution of Laplace partial differential equation
3.3.4 Boundary conditions
3.3.5 Solution for the dipolarizability
3.4 Limitations
4. Effective medium models of complex conductivity/permittivity of materials exhibiting various polarization phenomena
5. Surface-conductance-assisted interfacial polarization model: mechanistic model of conductivity/permittivity of porous mater ...
6. Validation of the surface-conductance-assisted interfacial polarization model
7. Surface-conductance-assisted interfacial polarization model predictions of multifrequency conductivity and permittivity in ...
7.1 The influence of the properties of the nonconductive particles
7.2 The influence of the conductivity of pore-filling electrolyte
7.3 The influence of the volume fractions of oil
8. Use of surface-conductance-assisted interfacial polarization model in subsurface/material characterization
9. Conclusions
Nomenclature
Acronyms
Symbols
Subscripts
Superscripts
References
4. Multifrequency conductivity and permittivity of porous material containing conductive particles in redox inactive conditions
1. Interfacial polarization phenomena around conductive particles in redox inactive conditions
2. Popular mechanistic models of interfacial polarization due to conductive particles in redox inactive conditions
3. Newly proposed mechanistic model of interfacial polarization due to conductive particles in redox inactive conditions
3.1 Model description
3.2 Assumptions
3.3 Model development
3.3.1 Poisson–Nernst–Planck equation
3.3.2 Solution of Helmholtz partial differential equation
3.3.3 Solution of Laplace partial differential equation
3.3.4 Boundary conditions
3.3.5 Solution for the dipolarizability
3.4 Limitations
4. Effective medium theory
5. Combining the perfectly polarized interfacial polarization (PPIP) model and the surface-conductance-assisted interfacial po ...
6. Validation of the PPIP–SCAIP (PS) model
7. PPIP–SCAIP (PS) model predictions of conductivity and permittivity versus frequency in 100Hz to 10MHz
7.1 The influence of the properties of the conductive particles
7.2 The influence of the properties of the mixture of conductive and nonconductive particles
7.3 The influence of the characteristic lengths of conductive and nonconductive particles
7.4 The influence of the volume fractions of conductive and nonconductive particles
7.5 The influence of the conductivity of pore-filling electrolyte
8. Use of PPIP–SCAIP model in subsurface/material characterization
9. Conclusions
Nomenclature
Acronyms
Symbols
Subscripts
Superscripts
References
5. Effects of wettability of conductive and nonconductive particles on the multifrequency electromagnetic response of porous m ...
1. Wettability of conductive and nonconductive particles and its influence on electromagnetic properties of fluid-filled porou ...
2. Wettability model for spherical conductive and nonconductive particles in two immiscible fluids
2.1 Model description
2.2 Assumptions
2.3 Model development
2.3.1 Far-field height of the interface
2.3.2 Young–Laplace equation for computing the shape of the interface around a spherical particle due to preferential-wettting co ...
2.3.3 Boundary conditions
2.3.4 Determination of wetting angle
2.3.5 Fractions of surface area of particle covered by water and oil
2.4 Limitations
3. Improved PS model: mechanistic model of conductivity/permittivity of porous material containing conductive and nonconductiv ...
4. Improved PS model predictions of conductivity and permittivity versus frequency
4.1 The porous material containing intermediately wet graphite
4.1.1 The influence of the contact angle of conductive particle
4.1.2 The influence of the wetting fluid saturation
4.1.3 The influence of the volume fraction of water-wet and oil-wet conductive particles
4.1.4 The influence of the radius of conductive particles
4.2 The porous material containing intermediately wet clay
4.2.1 The influence of the contact angle of nonconductive particle
4.2.2 The influence of the wetting fluid saturation
5. Conclusions
Nomenclature
References
Section 3
6. Unified deterministic inversion of multifrequency electromagnetic measurements using relaxation models
1. Introduction
2. Relaxation models
3. Previous studies on the deterministic-inversion-based interpretation of multifrequency electromagnetic measurements
4. Proposed unified deterministic inversion scheme
4.1 Nonlinear inversion as an error minimization problem
4.2 Damping parameter and iterative adjustment factor
4.3 Bounds of model parameters and jump-back-in step
4.4 Jump-out of local minimum step
5. Deterministic inversion of synthetic and laboratory electromagnetic measurements
5.1 Estimation of relaxation-model parameters by inverting synthetic electromagnetic data
5.2 Estimation of Havriliak–Negami model parameters by inverting laboratory electromagnetic data
5.3 Estimation of Cole–Cole model parameters by inverting laboratory electromagnetic measurements
5.4 Estimation of dual Cole–Cole model parameters by inverting laboratory electromagnetic measurements
6. Conclusions
Nomenclature
Symbols and abbreviations
References
7. Deterministic inversion of galvanic resistivity, induction resistivity, propagation resistivity, and dielectric dispersion logs
1. Introduction of multifrequency electromagnetic logs joint interpretation
2. Previous studies on deterministic interpretation of multifrequency permittivity and resistivity/conductivity measurements
3. Proposed modified bounded Levenberg–Marquardt nonlinear inversion scheme
3.1 Methodology
4. Sensitivity of PPIP-SCAIP model on synthetic layers
4.1 Sensitivity of PPIP-SCAIP model to water saturation
4.2 Sensitivity of PPIP-SCAIP model to salinity
4.3 Sensitivity of PPIP-SCAIP model to surface conductance of clay
4.4 Sensitivity of PPIP-SCAIP model to radius of spherical clay grain
4.5 Sensitivity of PPIP-SCAIP model to radius of spherical conductive mineral grain
5. Joint deterministic interpretation of multifrequency electromagnetic measurements
5.1 Inversion of synthetic logs generated at induction and dielectric dispersion frequencies
5.2 Inversion of synthetic logs generated at propagation and dielectric dispersion frequencies
6. Sensitivity analysis and accuracy of the joint deterministic interpretation method
6.1 Sensitivity analysis of inversion to factors λ and v implemented in the modified bounded Levenberg–Marquardt algorithm
6.2 Errors in inversion-derived estimates for various synthetic layers
6.3 Inversion-derived estimates when using various noise models
7. Application of the joint deterministic interpretation of multifrequency electromagnetic measurements in an organic-rich sha ...
Nomenclature
Symbols and abbreviations
References
Section 4
8. Stochastic inversion based interpretation of multifrequency electromagnetic logs from a European organic-rich shale formation
1. Introduction
1.1 The European organic-rich shale formation
1.2 Deployment of multiple electromagnetic logging tools
1.3 Limitations of conventional electromagnetic-log-interpretation models
1.4 Estimation of hydrocarbon saturation based on stochastic inversion of multifrequency electromagnetic logs
2. Stochastic inversion of multifrequency electromagnetic logs
2.1 Bayesian formulation
2.1.1 Bayesian framework
2.1.2 Prior distribution of model parameters p(m|I)
2.1.3 Likelihood function p(d|m,I)
2.2 Metropolis–Hastings sampling algorithms
2.2.1 Proposal distribution for sampling the unknown model parameters, q(m′|m)
2.2.2 Acceptance probability α(m|m’)
2.3 Convergence monitoring
3. Results and discussions
3.1 Application of the inversion-based interpretation method to synthetic layers
3.2 Sensitivity of PPIP-SCAIP model to volume fractions of clay and pyrite
3.3 Application of the inversion-based method to process broadband electromagnetic dispersion logs acquired in the European org ...
3.4 Petrophysical interpretation and log analysis of the inversion-derived estimates in the European organic-rich shale formation
4. Limitations and assumptions
5. Conclusions
Nomenclature
Symbols and abbreviations
References
9. Deterministic inversion based interpretation of multifrequency electromagnetic logs from wolfcamp and bakken shale formations
1. Introduction
2. Proposed deterministic inversion–based interpretation method
3. Sensitivity analysis of the proposed joint inversion scheme
3.1 Significance of the newly proposed joint inversion of galvanic/induction resistivity and dielectric dispersion logs
3.2 Uncertainties in inversion-derived estimates
3.3 Effect of pyrite in low-porosity, high-salinity formations
3.4 Threshold of brine conductivity in Waxman–Smits, Stroud-Milton-De, and complex refractive index model
4. Application of the newly proposed joint inversion on synthetic electromagnetic data
5. Application of the newly proposed joint inversion on multifrequency electromagnetic logs from Wolfcamp shale formation
5.1 Geology of Wolfcamp shale formation
5.2 Formation evaluation based on joint inversion of galvanic resistivity and dielectric dispersion logs
5.3 Analysis of interpretation errors
6. Application of the newly proposed joint inversion on multifrequency electromagnetic logs from Bakken Petroleum System
6.1 Geology of Bakken Petroleum System
6.2 Formation evaluation based on joint inversion of induction resistivity and dielectric dispersion logs
6.3 Analysis of interpretation errors
7. Limitations of the proposed interpretation of multifrequency electromagnetic logs
8. Conclusions
Symbols and abbreviations
References
Section 5
10. Multifrequency electromagnetic data interpretation using stochastic Markov-chain Monte Carlo and simulated annealing methods
1. Introduction
1.1 Markov-chain Monte Carlo inversion
1.2 Simulated annealing inversion
1.3 Petrophysical estimation based on stochastic inversion of multifrequency electromagnetic data
2. Method
2.1 The mechanistic electromagnetic model for subsurface characterization
2.2 The synthetic formation
2.3 Proposed inversion-based interpretation method
2.3.1 Markov-chain Monte Carlo inversion method
2.3.2 Simulated annealing inversion method
2.3.2.1 Method of generating the next solution
2.3.2.2 The cost function
2.3.2.3 Acceptance criterion
3. Results and discussions
4. Conclusions
Nomenclature
Acronyms
References
11. Multifrequency electromagnetic data interpretation using particle swarm optimization and ant colony optimization methods
1. Introduction
1.1 Particle swarm optimization
1.2 Ant colony optimization
1.3 Petrophysical estimation based on stochastic inversion of multifrequency electromagnetic data
2. Method
2.1 The mechanistic electromagnetic model for subsurface characterization
2.2 The synthetic formation
2.3 Proposed inversion-based interpretation method
2.3.1 Particle swarm optimization based inversion
2.3.1.1 Update of particle velocity
2.3.1.2 Update of particle location
2.3.1.3 Fitness function
2.3.2 Ant colony optimization-based inversion
2.3.2.1 Initialization of ant location
2.3.2.2 Objective function
2.3.2.3 Pheromone vector
2.3.2.4 Heuristic function
2.3.2.5 Possibility of ant movement
2.3.2.6 Update of ant location
2.3.2.7 Incremental pheromone
3. Results and discussions
4. Conclusions
Nomenclature
Acronyms
Symbols
Superscripts
Subscripts
References
Index